Finite time dead-core rate for the heat equation with a strong absorption
Guo, Jong-Shenq ; Wu, Chin-Chin
Tohoku Math. J. (2), Tome 60 (2008) no. 1, p. 37-70 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We study the solution of the heat equation with a strong absorption. It is well-known that the solution develops a dead-core in finite time for a large class of initial data. It is also known that the exact dead-core rate is faster than the corresponding self-similar rate. By using the idea of matching, we formally derive the exact dead-core rates under a dynamical theory assumption. Moreover, we also construct some special solutions for the corresponding Cauchy problem satisfying this dynamical theory assumption. These solutions provide some examples with certain given polynomial rates.
Publié le : 2008-05-15
Classification:  dead-core,  dead-core rate,  heat equation,  absorption,  35K57,  35K55,  34B16 
@article{1206734406,
     author = {Guo, Jong-Shenq and Wu, Chin-Chin},
     title = {Finite time dead-core rate for the heat equation with a strong absorption},
     journal = {Tohoku Math. J. (2)},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 37-70},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1206734406}
}

Guo, Jong-Shenq; Wu, Chin-Chin. Finite time dead-core rate for the heat equation with a strong absorption. Tohoku Math. J. (2), Tome 60 (2008) no. 1, pp.  37-70. http://gdmltest.u-ga.fr/item/1206734406/